# Circular Motion and Gravity

1. Oct 1, 2006

### thebigeis

Suppose a space station is constructed as a 1000m-diameter cylinder that rotates about its axis. What rotation period will provide "normal" gravity?

This is the work I have for this.

angular velocity = 9.8
r = 500m

2pi500/T = 9.8
2pi500/9.8 = T
T = 320.57

What did I do wrong?

2. Oct 1, 2006

### Andrew Mason

Why are you setting the angular velocity at 9.8? What are the units for angular velocity?

What is the centripetal force as a function of rotation speed or angular velocity and radius? Set that force is equal to the force of gravity.

AM

3. Oct 1, 2006

### thebigeis

I'm not given the angular velocity, so I'm assuming it's a number that I should already know. I don't have the mass either. Isn't "normal gravity" mass * acceleration, acceleration equaling 9.8m/s^2. This is why I'm confused. What I wrote above is all I'm given.

4. Oct 1, 2006

### Andrew Mason

So what is the centripetal acceleration in terms of rotational speed and radius? Set that equal to the (gravitational) acceleration you are trying to achieve. You are given the radius so you will be able to determine the angular speed needed to produce that centripetal acceleration.

AM

5. Oct 1, 2006

### thebigeis

a = v^2/r ... im pretty sure that's what you're asking
and then how can I get the angular speed if i don't have the period it takes for 1 revolution?

6. Oct 1, 2006

### thebigeis

Oh, wow, I figured out it out. Thanks a bunch, AM. You really helped me out.